Solve the following simultaneous equations:

$4x + \dfrac{x - y}{8} = 17, x + 2y = \dfrac{y - 2}{3} - 2$

Simplifying, equation : $4x + \dfrac{x - y}{8} = 17$

$\Rightarrow 4x + \dfrac{x - y}{8} = 17 \\[1em] \Rightarrow \dfrac{32x + x - y}{8} = 17 \\[1em] \Rightarrow (33x - y) = 17 \times 8 \\[1em] \Rightarrow (33x - y) = 136 \\[1em] \Rightarrow 33x - y = 136 \\[1em] \Rightarrow y = 33x - 136 \text{ ….(1)}$

Substituting value of y from equation (1) in $x + 2y = \dfrac{y - 2}{3} - 2$, we get :

$\Rightarrow x + 2y = \dfrac{y - 2}{3} - 2 \\[1em] \Rightarrow x + 2(33x - 136) = \dfrac{33x - 136 - 2}{3} - 2 \\[1em] \Rightarrow x + 66x - 272 = \dfrac{33x -138}{3} - 2 \\[1em] \Rightarrow 67x - 272 = \dfrac{3(11x - 46)}{3} - 2 \\[1em] \Rightarrow 67x - 272 = (11x - 46) - 2 \\[1em] \Rightarrow 67x - 272 = (11x - 48) \\[1em] \Rightarrow 67x - 11x = -48 + 272 \\[1em] \Rightarrow 56x = 224 \\[1em] \Rightarrow x = \dfrac{224}{56} = 4.$

Substituting value of y in equation (1), we get :

⇒ y = 33(4) - 136

⇒ y = 132 - 136

⇒ y = -4.

Hence, x = 4, y = -4.